Solve: 2x+7/5 - x-3/10 = x+1/15find the value of x and verify the result will RHS
2 answers:
Step-by-step explanation:
<h3><u>Given Question :- </u></h3>Solve for x :-
Given linear equation is
On multiply by 5 on both sides,
On cross multiplication, we get
Consider, LHS
On substituting the value of x, we get
Consider RHS
On substituting the value of x, we get
HENCE, VERIFIED
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Let's go step by step:
a) You are given four couples of x and y values which model the relationship between the number of drinks and their cost. So, the couple means that if you buy zero drinks, you spend no money. That makes sense. The next information we have is
, which means that two drinks cost 3 dollars, and so on.
So, you simply need to draw on the grid the four points
b) The domain is the set of inputs. Since we only know the value of the function on four different points (we know the price for 0,2,4 and 6 drinks), the domain is discrete. In fact, a continuous domain must contain an interval (for example, is a continuous domain), whereas if you pick a certain number of points (like in this case: we picked 0,2,4 and 6), the domain is discrete.
c) Once the points are drawn on the grid, you can see that they all lie on the same line. To find that line, we will only need two of those points (once two points are fixed, there is only one line passing through them). In general, the equation of the line passing through and
is
Let's choose, for example, the first two points. The equation is
d) Now that we know the equation of the line, we can compute the cost of any number of drinks: the equation of the line is a function that associates a cost, y, with every possible number of drinks, x.
Of course, some associations will be odd - we can compute the cost of drink, but what would it mean?
Anyway, the question about the cost of two drinks seems more than reasonable, so let's see which y value is associate with the particular x value of 2:
So, two drinks cost 3 dollars.
Answer:
Step-by-step explanation:
Hello!
a)
The variable of interest is
X: monetary value of a grab bag. ($)
The possible values this variable can take are:
X: 15; 40; 60; 120
To calculate the relative frequency of each possible value of the variable you have to divide the number of times this value is observed by the total of observations (sample size)
There where a total of 300 bags created, from these, 40 cost $40, 20 cost $60, 1 cost $120, and the rest have a monetary value of $15.
There are then 300- (40+20+1)= 239 bags with a monetary value of $15
The frequencies for each value of X are:
X= 15 ⇒ p(X)= 239/300= 0.797
X= 40 ⇒ p(X)= 40/300= 0.133
X= 60 ⇒ p(X)= 20/300=0.067
X= 120⇒ p(X)= 1/300= 0.003
The probability distribution for X is:
Xi: 15; 40; 60; 120
p(Xi):0.797; 0.133; 0.067; 0.003
∑p(Xi)= 0.797+0.133+0.067+0.003=1
b)
To calculate the mean you have to use the following formula:
E(X)= ∑Xp(X)= 15*0.797+40*0.133+60*0.067+120*0.003= 21.655≅ $21.7
c)
The standard deviation is the square root of the variance:
Variance:
V(X)= ∑X²p(X)-(∑Xp(X))²= 676.525 - (21.655)²= 207.585
∑X²p(X)= 15²*0.797+40²*0.133+60²*0.067+120²*0.003= 676.525
Standard deviation:
√V(X)= √207.585= $14.407= $14.41
d)
Considered the probability distribution, it is more likely to buy a $15 worth bag than any of the others, it is therefore not worthwhile to spend $20 in a bag full of merchandise worth $15.
I hope this helps!
